Transcript Step 2.

Contemporary Mathematics
for Business and Consumers
Third Edition
By: Robert A. Brechner
COPYRIGHT © 2003 by South-Western, a division of Thomson Learning. Thomson LearningTM is a
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Chapter 2
Fractions
Copyright © 2003 by South-Western
CHAPTER 2
Fractions
SECTION I: Understanding and Working with Fractions
2-1 Distinguishing among the various types of fractions.
2-2 Converting improper fractions to whole or mixed numbers.
2-3 Converting mixed numbers to improper fractions.
2-4 Reducing fractions to lowest terms using
a. Inspection and the rules of divisibility.
b. The greatest common divisor method.
2-5 Raising fractions to higher terms.
SECTION II: Addition and Subtraction of Fractions
2-6 Determining the least common denominator (LCD) of two or
more fractions.
2-7 Adding fractions and mixed numbers.
CHAPTER 2
Fractions (cont.)
SECTION II: Addition and Subtraction of Fractions
2-8 Subtracting factions and mixed numbers
SECTION III: Multiplication and Division of
Fractions
2-9 Multiplying fractions and mixed numbers.
2-10 Dividing fractions and mixed numbers.
Chapter 2, Section I
Numerator :
The number on top of the division line of a fraction. It represents the
divided in the division. In the fraction ¼, 1 is the denominator.
Denominator:
The number on the bottom of the division line of a fraction. It
represents the divisor in the division. In the fraction 1/4 , 4 is the
denominator.
Division line:
The horizontal or slanted line separating the numerator from the
denominator. The symbol representing “divided by” in a fraction. In
the fraction ¼, the line between the 1 and the 4 is the division line.
Common or Proper fraction:
A fraction in which the numerator is smaller to or less than the
numerator. Represents one whole unit or more. The fraction 4/1 is
an improper fraction.
Mixed Number:
A number that combines a whole number with a proper fraction.
The fraction 101/4 is a mixed number.
Everybody’s Business
A complex fraction is one in which the numerator of
the denominator, or both, are fractions
Examples: 2/3
6
9
¾
7/8
1/4
2-2 Converting Improper Fractions to Whole or
Mixed Numbers
Steps for Converting Improper Fractions to Whole or Mixed
Numbers.
Step 1. Divide the Numerator of the improper fraction by the
denominator.
Step 2a. If there is no remainder, the improper fraction
becomes a whole number.
Step 2b. If there is a remainder, write the whole number and
then write the fraction.
Whole number = Remainder
Divisor
2-3 Converting Mixed Numbers to Improper
Fractions
Steps for Converting a Mixed Number to an Improper
Fraction:
Step 1. Multiply the denominator by the whole
number.
Step 2. Add the numerator to the product from Step
1.
Step 3. Place the total from Step 2 as the “new”
numerator.
Step 4. Place the original denominator as the “new”
denominator.
2-4 Reducing Fractions to Lowest Terms
Steps for Determining the Greatest Common
Divisor of a Fraction:
Step 1. Divide the number of the fractin into the denominator.
Step 2. Take the remainder from Step 1 and divide it into the
divisor from Step 1.
Step 3. Repeat this division process until the remainder is
either 0 or 1.
 If the remainder is 0, the last divisor is the greatest
common divisor.
 If the remainder is 1, the fraction cannot be reduced and is
therefore in lowest terms
2-5 Raising Fractions to Higher Terms
Steps for Raising A Fraction To A New Denominator:
Step 1. Divide the original denominator into the new
denominator. The resulting quotient is the common multiple
that raises the fraction.
Step 2. Multiply the numerator and the denominator of the
original fraction by the common multiple.
Section II, Addition And Subtraction of
Fractions
2-6 Determining the last Common Denominator (LCD) of
Two or More Fractions
Steps for Finding the Least Common Denominator of Two or More
Fractions:
Step 1. Write all the denominators in a row.
Step 2. Find a prime number that divides evenly into any of the
denominators. Write that prime number to the left of the row, and
divide. Place all quotients and undivided numbers in the next row
down.
Step 3. Repeat this process until the new row contains all ones.
Step 4. Multiply all the prime numbers oin the left together to get
the LCD of the fractions.
EVERYBODY’S BUSINESS
Answer to fraction problems should
always be reduced to lowest terms
2-7 Adding Fractions with the Same
Denominator
Steps for Adding Like Fractions:
Step 1. Add all the numerators and place the total over the
original denominator.
Step 2. If the result is a proper fraction, reduce it to lowest
terms.
Step 3. If the result is an improper fraction, convert it to a
whole or a mixed number.
Adding Fractions With Different Denominators
Steps for Adding Unlike Fractions:
Step 1. Find the least common denominator of the
unlike fractions.
Step 2. Raise all fractions to the terms of the LCD,
making them like fractions.
Step 3. Follow the same procedure used for adding
like fractions.
Adding Mixed Numbers
Steps for Adding Mixed Numbers:
Step 1. Add the fractional parts. If the sum is an
improper fraction, convert it to a mixed number.
Step 2. Add the whole number.
Step 3. Add the fraction from Step 1 to the whole
number from Step 2.
Step 4. Reduce the sum to lowest terms.
2-8 Subtracting Fractions and Mixed
Numbers
Steps for Subtracting Like Fractions:
Step 1. Subtract the numerators and place the difference over
the original denominator.
Step 2. Reduce the fractions to lowest terms.
Steps for Subtracting Unlike Fractions:
Step 1. Find the least common denominator.
Step 2. Raise each fractin to the denominator of the LCD.
Step 3. Follow the same procedure used to subtract like
fractions.
Subtracting Mixed Numbers
Steps for Subtracting Mixed Numbers:
Step 1. If the fractions of the mixed numbers have
the same denominator, subtract them and reduce
to lowest terms.
Step 2. If the fractions do not have the same
denominator, raise them to the denominator of the
LCD, and subtract.
Step 3. Subtract the whole numbers.
Step 4. Add the difference of the whole numbers
and the difference of the fractions.
SECTION III, Multiplications and Division
of Fractions
2-9 Multiplying Fractions:
Step 1. Multiply all numerators to form the new
numerator.
Step 2. Multiply all the denominators to form the
new denominator.
Step 3. If necessary, reduce the answers to lowest
terms.
SECTION III, Multiplications and Division
of Fractions
2-9 Steps for Applying Cancellation:
Step 1. Find a common factor that devides evenly
into at least one of the denominators and one of
the numerators.
Step 2. Divide that common factor into the
denominator and numerator, thereby reducing it.
Step 3. Repeat this process until there are no more
common factors.
Step 4. Multiply the fractions as before.
Multiplying Mixed Numbers
2-9 Steps for Multiplying Mixed Numbers:
Step 1. Convert all mixed numbers to improper
fractions.
Step 2. Multiply as before, using cancellation
wherever possible..
Step 3. If the answer is an improper fraction,
convert it to a whole or mixed number.
Step 4. Reduce to lowest terms..
2-10 Dividing Fractions and Mixed
Numbers
Steps for Dividing Fractions:
Step 1. Identify the fraction that is the divisor, and
invert.
Step 2. Change the”divide by” sign, to a “multiplied
by” sign x.
Step 3. Multiply the fractions.
Step 4. Reduce the answer to lowest terms.
EVERYBODY’S BUSINESS
The number after the “divide sign” is the
divisor.
This is the number that gets inverted
when dividing.